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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (43 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3381.1.c.a	$3381$	$1$	3381.c	483.c	$2$	$8$	$8$	$1.687$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-23}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{16}^{2}+\zeta_{16}^{6})q^{2}-\zeta_{16}q^{3}-q^{4}+\cdots$
3381.1.c.b	$3381$	$1$	3381.c	483.c	$2$	$16$	$16$	$1.687$	$\Q(\zeta_{48})$	$D_{24}$	$\Q(\sqrt{-23}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{48}^{2}-\zeta_{48}^{22})q^{2}+\zeta_{48}^{5}q^{3}+\cdots$
3381.1.o.a	$3381$	$1$	3381.o	483.o	$6$	$16$	$8$	$1.687$	$\Q(\zeta_{48})$	$D_{24}$	$\Q(\sqrt{-23}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{48}^{6}-\zeta_{48}^{10})q^{2}-\zeta_{48}^{9}q^{3}+(\zeta_{48}^{12}+\cdots)q^{4}+\cdots$
3381.1.o.b	$3381$	$1$	3381.o	483.o	$6$	$16$	$8$	$1.687$	$\Q(\zeta_{48})$	$D_{24}$	$\Q(\sqrt{-23}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{48}^{18}-\zeta_{48}^{22})q^{2}+\zeta_{48}^{5}q^{3}+\cdots$
3381.1.o.c	$3381$	$1$	3381.o	483.o	$6$	$16$	$8$	$1.687$	$\Q(\zeta_{48})$	$D_{8}$	$\Q(\sqrt{-23}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{48}^{10}-\zeta_{48}^{22})q^{2}+\zeta_{48}^{5}q^{3}+\cdots$
3381.2.a.a	$3381$	$2$	3381.a	1.a	$1$	$1$	$1$	$26.997$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+3q^{8}+\cdots$
3381.2.a.b	$3381$	$2$	3381.a	1.a	$1$	$1$	$1$	$26.997$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+3q^{5}+q^{6}+3q^{8}+\cdots$
3381.2.a.c	$3381$	$2$	3381.a	1.a	$1$	$1$	$1$	$26.997$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$1$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-3q^{5}-q^{6}+3q^{8}+\cdots$
3381.2.a.d	$3381$	$2$	3381.a	1.a	$1$	$1$	$1$	$26.997$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots$
3381.2.a.e	$3381$	$2$	3381.a	1.a	$1$	$1$	$1$	$26.997$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{9}-2q^{11}+2q^{12}+\cdots$
3381.2.a.f	$3381$	$2$	3381.a	1.a	$1$	$1$	$1$	$26.997$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{9}+5q^{11}+2q^{12}+\cdots$
3381.2.a.g	$3381$	$2$	3381.a	1.a	$1$	$1$	$1$	$26.997$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{9}+6q^{11}+2q^{12}+\cdots$
3381.2.a.h	$3381$	$2$	3381.a	1.a	$1$	$1$	$1$	$26.997$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{9}-2q^{11}-2q^{12}+\cdots$
3381.2.a.i	$3381$	$2$	3381.a	1.a	$1$	$1$	$1$	$26.997$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{9}+5q^{11}-2q^{12}+\cdots$
3381.2.a.j	$3381$	$2$	3381.a	1.a	$1$	$1$	$1$	$26.997$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{9}+6q^{11}-2q^{12}+\cdots$
3381.2.a.k	$3381$	$2$	3381.a	1.a	$1$	$1$	$1$	$26.997$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots$
3381.2.a.l	$3381$	$2$	3381.a	1.a	$1$	$1$	$1$	$26.997$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$-1$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-4q^{5}-2q^{6}+\cdots$
3381.2.a.m	$3381$	$2$	3381.a	1.a	$1$	$1$	$1$	$26.997$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$2$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-2q^{6}+q^{9}+q^{11}+\cdots$
3381.2.a.n	$3381$	$2$	3381.a	1.a	$1$	$2$	$2$	$26.997$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$-3$	$-2$	$5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(2+\beta )q^{5}+\cdots$
3381.2.a.o	$3381$	$2$	3381.a	1.a	$1$	$2$	$2$	$26.997$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$-5$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-3+\beta )q^{5}+\cdots$
3381.2.a.p	$3381$	$2$	3381.a	1.a	$1$	$2$	$2$	$26.997$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$5$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+(3-\beta )q^{5}+\cdots$
3381.2.a.q	$3381$	$2$	3381.a	1.a	$1$	$2$	$2$	$26.997$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+\beta q^{5}+\beta q^{6}+\cdots$
3381.2.a.r	$3381$	$2$	3381.a	1.a	$1$	$2$	$2$	$26.997$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$2$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots$
3381.2.a.s	$3381$	$2$	3381.a	1.a	$1$	$2$	$2$	$26.997$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$2$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(2+\beta )q^{4}-\beta q^{5}-\beta q^{6}+\cdots$
3381.2.a.t	$3381$	$2$	3381.a	1.a	$1$	$2$	$2$	$26.997$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+3q^{4}+(1-\beta )q^{5}-\beta q^{6}+\cdots$
3381.2.a.u	$3381$	$2$	3381.a	1.a	$1$	$2$	$2$	$26.997$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(1+\beta )q^{5}+\cdots$
3381.2.a.v	$3381$	$2$	3381.a	1.a	$1$	$3$	$3$	$26.997$	3.3.837.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
3381.2.a.w	$3381$	$2$	3381.a	1.a	$1$	$4$	$4$	$26.997$	4.4.24197.1	$_{}$	None	None	✓	$1$	$1$	$0$	$4$	$-5$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots$
3381.2.a.x	$3381$	$2$	3381.a	1.a	$1$	$4$	$4$	$26.997$	4.4.15317.1	$_{}$	None	None	✓	$1$	$0$	$2$	$4$	$-5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$
3381.2.a.y	$3381$	$2$	3381.a	1.a	$1$	$5$	$5$	$26.997$	5.5.3176240.1	$_{}$	None	None	✓	$1$	$1$	$1$	$-5$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots$
3381.2.a.z	$3381$	$2$	3381.a	1.a	$1$	$5$	$5$	$26.997$	5.5.3176240.1	$_{}$	None	None	✓	$1$	$0$	$1$	$5$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
3381.2.a.ba	$3381$	$2$	3381.a	1.a	$1$	$6$	$6$	$26.997$	6.6.62622704.1	$_{}$	None	None	✓	$1$	$0$	$-3$	$-6$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
3381.2.a.bb	$3381$	$2$	3381.a	1.a	$1$	$6$	$6$	$26.997$	6.6.62622704.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$6$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
3381.2.a.bc	$3381$	$2$	3381.a	1.a	$1$	$6$	$6$	$26.997$	6.6.7997584.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-6$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(\beta _{3}+\beta _{5})q^{5}+\cdots$
3381.2.a.bd	$3381$	$2$	3381.a	1.a	$1$	$6$	$6$	$26.997$	6.6.7997584.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$6$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$
3381.2.a.be	$3381$	$2$	3381.a	1.a	$1$	$8$	$8$	$26.997$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$-8$	$-5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{7})q^{5}+\cdots$
3381.2.a.bf	$3381$	$2$	3381.a	1.a	$1$	$8$	$8$	$26.997$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$8$	$5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{7})q^{5}+\cdots$
3381.2.a.bg	$3381$	$2$	3381.a	1.a	$1$	$10$	$10$	$26.997$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-4$	$-10$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$
3381.2.a.bh	$3381$	$2$	3381.a	1.a	$1$	$10$	$10$	$26.997$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-4$	$10$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{3}-\beta _{8}+\cdots)q^{5}+\cdots$
3381.2.a.bi	$3381$	$2$	3381.a	1.a	$1$	$10$	$10$	$26.997$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$-10$	$-5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{8}+\cdots)q^{5}+\cdots$
3381.2.a.bj	$3381$	$2$	3381.a	1.a	$1$	$10$	$10$	$26.997$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$10$	$5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{8}+\cdots)q^{5}+\cdots$
3381.2.a.bk	$3381$	$2$	3381.a	1.a	$1$	$10$	$10$	$26.997$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$4$	$-10$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots$
3381.2.a.bl	$3381$	$2$	3381.a	1.a	$1$	$10$	$10$	$26.997$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$4$	$10$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.